This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ( t ) , then eliminate v to give the streamlines in the form u = H ( v ) . Sketch several curves. 5. [18] (a) Find the Fourier transform, justify all steps carefully g ( x ) = e −  x  , − ∞ < x < ∞ . (b) Use a Fourier transform to solve u tt + 2 u t + u = u xx , − ∞ < x < ∞ , < t, u ( x, 0) = e −  x  , u t ( x, 0) = 0 , − ∞ < x < ∞ . Write the solution in the form u ( x, t ) = Z ∞ G ( x, t, ω ) dω. 6. [18] (a) Find the inverse Laplace transform, justify all steps carefully G ( x, t ) = L − 1 ( e − x √ s √ s ) (c) Use a Laplace transform to f nd the solution to the problem: u t = u xx , < x < ∞ , < t, u ( x, 0) = , u (0 , t ) = 1 √ t , t > . You may use the results Z ∞ e − r 2 dr = √ π 2 ; Z ∞ 1 √ u e − au du = r π a . 2...
View
Full
Document
This note was uploaded on 01/23/2011 for the course MATH 100,200,30 taught by Professor Dr.alejandrocortas during the Winter '10 term at UBC.
 Winter '10
 Dr.AlejandroCortas
 Math, Integrals

Click to edit the document details